cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A165419 Each a(n) is chosen so that n = sum a(k), for all n >= 0, where k is over the distinct nonnegative values of the substrings in binary n.

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%I A165419 #7 Mar 11 2014 01:32:48
%S A165419 0,1,1,2,2,3,2,4,4,5,5,4,4,4,4,8,8,9,9,8,8,11,9,8,8,8,8,10,8,8,8,16,
%T A165419 16,17,17,16,18,16,17,16,16,16,21,16,16,19,17,16,16,16,16,18,16,16,18,
%U A165419 16,16,16,16,16,16,16,16,32,32,33,33,32,34,32,33,32,32,37,32,32,34,32,33
%N A165419 Each a(n) is chosen so that n = sum a(k), for all n >= 0, where k is over the distinct nonnegative values of the substrings in binary n.
%C A165419 We could have instead taken k over the distinct positive values of the substrings in binary n, and get the same sequence, since a(0)=0.
%C A165419 The distinct nonnegative values of the substrings of binary n is row n of table A119709. The distinct positive values of the substrings of binary n is row n of table A165416.
%e A165419 9 in binary is 1001. The distinct nonnegative integers that occur as substrings in binary 9 are 0, 1, 2 (10 in binary), 4 (100 in binary), and 9 (1001 in binary). And 9 = a(0) + a(1) + a(2) + a(4) + a(9) = 0 + 1 + 1 + 2 + 5.
%Y A165419 Cf. A119709, A165416.
%K A165419 base,nonn
%O A165419 0,4
%A A165419 _Leroy Quet_, Sep 17 2009
%E A165419 Extended by _Ray Chandler_, Mar 13 2010